The -invariant of Seifert fibered homology spheres and the Dirac operator

The -invariant of Seifert fibered homology spheres and the Dirac operator

We derive a formula for the -invariant of a Seifert fibered homology sphere in terms of the η -invariant of its Dirac operator. As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres.

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Veröffentlicht in:Geometriae dedicata 2011-10, Vol.154 (1), p.93-101
Hauptverfasser: Ruberman, Daniel, Saveliev, Nikolai
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Beschreibung
Zusammenfassung:We derive a formula for the -invariant of a Seifert fibered homology sphere in terms of the η -invariant of its Dirac operator. As a consequence, we obtain a vanishing result for the index of certain Dirac operators on plumbed 4-manifolds bounding such spheres.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-010-9569-5